Eigenvalue Estimates for Schrödinger Operators with Complex Potentials
By Ari Laptev, Oleg Safronov. 2009
116 citations recorded by the source corpus.
We discuss properties of eigenvalues of non-self-adjoint Schrödinger operators with complex-valued potential V. Among our results are estimates of the sum of powers of imaginary parts of eigenvalues by the Lp-norm of $${{\Im{V}}}$$.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5df54598280d3e01eec488ffedb884c2c9fa0593
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In Mathematical Physics
- Barry Simon
- Julien Sabin
- Rupert L. Frank
- Doron S. Lubinsky
- David Damanik
- David Damanik
- Alexander Pushnitski
- Vilmos Totik
Citations in the corpus
- Eigenvalue bounds for Schrödinger operators with complex potentials. II (2015, background): “If Laptev and Safronov had formulated their conjecture for any eigenvalueE 2 C (and not only forE 2 CnŒ0;1/), we would have disproved it.”
- Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates (2014, background): “Eigenvalues bounds for Schr¨odinger operators with complex-valued potentials have been the topic of many works, see for instance [1, 11, 23, 5, 10] and references therein.”